1988 AMC 8 Problem 20

Attempt Problem 20 of the 1988 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

20.

The glass gauge on a cylindrical coffee maker shows there are 4545 cups left when the coffee maker is 36%36\% full. How many cups of coffee does it hold when it is full?
8080
100100
125125
130130
262262
Answer: C
Concepts:percentageratio and proportion
Small hint:
Set up a proportion: 4545 cups is to the full amount as 3636 is to 100100
Big hint:
If 36%36\% is 4545 cups, first find how many cups 4%4\% is
Solution:
Let nn be the full capacity. Then 45n=36100.\dfrac{45}{n} = \dfrac{36}{100}.
Solving, n=45×10036=125n = \dfrac{45 \times 100}{36} = 125 cups.
Thus, the correct answer is C .
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